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We give results of recent work on a newly developed frequency stability characterization, called Total variance, whose main advantages are improved confidence at and near the longest averaging time of half the data duration, and lower sensitivity to drift removal.
The sun exhibits periodic and quasi-periodic variability in its total luminosity, which provides information about its internal structure and dynamics. Variability ranges from a few minutes to many-year time scales, with amplitudes as small as a few ppm in the milliHz band. Extension of this analysis to a large sample of outer stars would be interesting: a panoramic detector such as a CCD could record many stars at once. To meet this objective, a ppm time-series differential precision is required. Laboratory CCD photometric measurements presented here are promising for such an instrument. Normalizing the response from a portion of the CCD area removes most of the individual-frame variability. When a trend attributed to a thermal transient in the CCD dewar is removed, the individual-frame photometric precision is about 0.0001, limited by photoelectron counting statistics. The time-series power spectrum is flat within the desired frequency domain. Analysis of the dimensional stability of the CCD within the same data set indicates better than ppm performance, when first-order bulk motion and magnification changes are removed.
Arm locking is a technique that has been proposed for reducing laser frequency fluctuations in the Laser Interferometer Space Antenna (LISA). a gravitational-wave observatory sensitive' in the milliHertz frequency band. Arm locking takes advantage of the geometric stability of the triangular constellation of three spacecraft that comprise LISA to provide a frequency reference with a stability in the LISA measurement band that exceeds that available from a standard reference such as an optical cavity or molecular absorption line. We have implemented a time-domain simulation of arm locking including the expected limiting noise sources (shot noise, clock noise. spacecraft jitter noise. and residual laser frequency noise). The effect of imperfect a priori knowledge of the LISA heterodyne frequencies and associated "pulling" of an arm locked laser is included. We find that our implementation meets requirements both on the noise and dynamic range of the laser frequency.
When designing and certifying aircraft, engineers must take into consideration aeroelastic effects such as flutter. Design and certification of a vehicle may require analysis of thousands of aeroelastic responses. Standard tools in the aerospace industry are based on linear aerodynamic models such as the doublet-lattice method, but these methods can be nonconservative in certain situations such as in the transonic regime. While computational fluid dynamics (CFD) is a higher fidelity alternative, the time-marching approach has a drastically increased computational cost compared to the linear aerodynamic methods. By taking advantage of the periodic nature of flutter, frequency-domain methods offer a more efficient alternative to time-marching CFD. In this work, a linearized frequency-domain method is implemented and verified in the stabilized finite-element solver in FUN3D. The linearized frequency-domain method is demonstrated and compared to other methods for traditional benchmark cases for computational aeroelasticity: the AGARD 445.6 wing, the Benchmark Supercritical Wing, and the Benchmark NACA 0012Wing.
This paper presents a dynamic stability estimation technique obtained from high-fidelity CFD simulations of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). A series of unsteady RANS CFD simulations in FUN3D is performed on the TTBW in pitch and plunge oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain regression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with respect to the pitch rate are deter-mined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. The steady-state stability derivatives are then compared to the results obtained from a stability analysis code VSPAERO as well as steady-state FUN3D simulations. The comparison of the steady-state stability derivatives shows excellent agreement.
We report on the development, functional performance and space-qualification status of a laser stabilization system supporting a space-based metrology source used to measure changes in optical path lengths in space-based stellar interferometers. The Space Interferometry Mission (SIM) and Deep Space 3 (DS-3) are two missions currently funded by the National Aeronautics and Space Administration (NASA) that are space-based optical interferometers. In order to properly recombine the starlight received at each telescope of the interferometer it is necessary to perform high resolution laser metrology to stabilize the interferometer. A potentially significant error source in performing high resolution metrology length measurements is the potential for fluctuations in the laser gauge itself. If the laser frequency or wavelength is changing over time it will be misinterpreted as a length change in one of the legs of the interferometer. An analysis of the frequency stability requirement for SIM resulted in a fractional frequency stability requirement of square root (S(sub y)(f)) = <2 x 10(exp -12)/square root(Hz) at Fourier frequencies between 10 Hz and 1000 Hz. The DS-3 mission stability requirement is further increased to square root (S(sub y)(f)) = <5 x 10(exp -14)/Square root(Hz) at Fourier frequencies between 0.2 Hz and 10 kHz with a goal of extending the low frequency range to 0.05 Hz. The free running performance of the Lightwave Electronics NPRO lasers, which are the baseline laser for both SIM and DS-3 vary in stability and we have measured them to perform as follows (9 x l0(exp -11)/ f(Hz))(Hz)/square root(Hz)) = <( square root (S(sub y)(f)) = <(1.3 x l0(exp -8)/ f(Hz))/Square root(Hz). In order to improve the frequency stability of the laser we stabilize the laser to a high finesse optical cavity by locking the optical frequency of the laser to one of the transmission modes of the cavity. At JPL we have built a prototype space-qualifiable system meeting the stability requirements of SIM, which has been delivered to one of the SIM testbeds. We have also started on the development of a system to meet the stability needs of DS-3.
In order to develop a trapped ion-based fieldable frequency standard with stability 1 x 10 to the -13th/sq rt tau for averaging times tau greater than 10,000 s, a hybrid RF/DC linear ion trap was developed which permits storage of large numbers of ions with reduced susceptibility to the second-order Doppler effect caused by the RF confining fields. The authors have confined Hg-199(+) ions in this trap and have measured very high Q transitions with good SNRs. In preliminary measurements they obtained stabilities of 1.6 x 10 to the -13th/sq rt tau (tau between 50 and 800 s) with a 160-mHz wide atomic resonance linewidth and a signal-to-noise ratio of 40 for each measurement cycle. Atomic resonance lines as narrow as 30 mHz on the 40.5-GHz clock transition have been measured with no appreciable reduction in the ion signal. A stability of 7 x 10 to the -14th/sq rt tau is made possible by the signal-to-noise and line Q of this measured transition. Analysis of fundamental sources of frequency instability indicates that a long-term stability of 2 x 10 to the -16th is feasible for this device with existing technology for tau = 10 to the 6th s or more.
A matrix method is presented for determining the longitudinal-stability coefficients and frequency response of an aircraft from arbitrary maneuvers. The method is devised so that it can be applied to time-history measurements of combinations of such simple quantities as angle of attack, pitching velocity, load factor, elevator angle, and hinge moment to obtain the over-all coefficients. Although the method has been devised primarily for the evaluation of stability coefficients which are of primary interest in most aircraft loads and stability studies, it can be used also, with a simple additional computation, to determine the frequency-response characteristics. The entire procedure can be applied or extended to other problems which can be expressed by linear differential equations.
The design, analysis, and experimental evaluation of an optimum performance torque current generator for use with strapdown gyroscopes, is presented. Among the criteria used to evaluate the design were the following: (1) steady-state accuracy; (2) margins of stability against self-oscillation; (3) temperature variations; (4) aging; (5) static errors drift errors, and transient errors, (6) classical frequency and time domain characteristics; and (7) the equivalent noise at the input of the comparater operational amplifier. The DC feedback loop of the torque current generator was approximated as a second-order system. Stability calculations for gain margins are discussed. Circuit diagrams are shown and block diagrams showing the implementation of the torque current generator are discussed.
The capabilities of the Marshall system for aerospace system simulation (MARSYAS) and how to use it are described. MARSYAS is a software system that allows easy setup and control of the simulation of the dynamics of large physical systems on a digital computer. The physical systems are modeled in the form of block diagrams or equations. The blocks can have multiple inputs and multiple outputs, and they can be nested to form hierarchies. The block diagrams can contain transfer functions, nonlinear and logical functions, equations, analog computer elements and FORTRAN programs. The input format of the equations can be combinations of nonlinear, time-varying differential equations and algebraic equations in their original format. MARSYAS could also serve as a storage and retrieval system for models as a basis for a model configuration control system on a central time-shared computer. The outputs of the simulation system can be not only time-responses but also other analysis data such as frequency response, power spectrum and stability parameters. The MARSYAS translator is written in FORTRAN running on the Univac 1108 computer under the EXEC 8 operating system.
The development of a particulate mass-sensing instrument based on a quartz-crystal microbalance and enhanced with the new surface acoustic-wave (SAW) technology is reported. Mass sensitivity comparisons of a 158-MHz SAW piezoelectric microbalance and a conventional 10-MHz quartz-crystal microbalance show that the SAW crystal is 266 times more sensitive, in good agreement with the theoretical value of 250. The frequency stability of a single SAW resonator is 6 parts in 10 to the 8th over 1 min. The response to temperature changes is found to be very linear over the range +30 to -30 C. A strong response to 15 ppm SO2 has been demonstrated on a chemically coated SAW crystal.
A new integration algorithm which has the simplicity of Euler integration but exhibits second-order accuracy is described. In fixed-step numerical integration of differential equations for mechanical dynamic systems the method represents displacement and acceleration variables at integer step times and velocity variables at half-integer step times. Asymptotic accuracy of the algorithm is twice that of trapezoidal integration and ten times that of second-order Adams-Bashforth integration. The algorithm is also compatible with real-time inputs when used for a real-time simulation. It can be used to produce simulation outputs at double the integration frame rate, i.e., at both half-integer and integer frame times, even though it requires only one evaluation of state-variable derivatives per integration step. The new algorithm is shown to be especially effective in the simulation of lightly-damped structural modes. Both time-domain and frequency-domain accuracy comparisons with traditional integration methods are presented. Stability of the new algorithm is also examined.
The spectrum of tropospheric delay fluctuations expected for a DSN antenna at time scales less than 100 s has been calculated. A new feature included in these calculations is the effect of aperture averaging, which causes a reduction in delay fluctuations on time scales less than the antenna wind speed crossing time, approximately equal to 5-10 s. On time scales less than a few seconds, the Allan deviation sigma(sub y)(Delta(t)) varies as (Delta(t))(sup +1), rather than sigma(sub y)(Delta(t)) varies as (Delta(t))(exp -1/6) without aperture averaging. Due to thermal radiometer noise, calibration of tropospheric delay fluctuations with water vapor radiometers will not be possible on time scales less than approximately 10 s. However, the tropospheric fluctuation level will be small enough that radio science measurements with a spacecraft on time scales less than a few seconds will be limited by the stability of frequency standards and/or other nontropospheric effects.
The spectrum of tropospheric delay fluctuations expected for a DSN antenna at time scales less than 100 s has been calculated. A new feature included in these calculations is the effect of aperture averaging, which causes a reduction in delay fluctuations on time scales less than the antenna wind speed crossing time, approx. equal to 5-10 s. On time scales less than a few seconds, the Allan deviation sigma(y)(Delta(t)) is proportional to (Delta(t))(exp +1), rather than sigma(y)(Delta(t)) proportional to (Delta(t))(exp -1/6) without aperture averaging. Due to thermal radiometer noise, calibration of tropospheric delay fluctuations with water vapor radiometers will not be possible on time scales less than approx. equal to 10 s. However, the tropospheric fluctuation level will be small enough that radio science measurements with a spacecraft on time scales less than a few seconds will be limited by the stability of frequency standards and/or other nontropospheric effects.
This paper discusses the use of an adaptive system to stabilize a multi-tank launch vehicle with sloshable fuel. The adaptive system utilizes a sensor to measure the fluid slosh angle, a recursive-least-squares estimator to estimate the natural frequency of the sloshing fuel, and a linear filter which stabilizes the unstable fuel slosh using the frequency estimate. Single-input and multiinput estimators were investigated. The time-varying complexity of the slosh control loop keeps the system persistently excited through flight, even though the attitude is controlled by a conventional PID controller. For the first portion of flight, the adaptive system maintains stability. A modification is proposed for latter portions of flight. The approach requires no tank baffles or partitions.
A technique for predicting the stability characteristics of a gaseous-propellant rocket combustion system is developed based on a model that assumes coupling between the flow through the injector and the oscillating chamber pressure. The theoretical model uses a lumped parameter approach for the flow elements in the injection system plus wave dynamics in the combustion chamber. The injector flow oscillations are coupled to the chamber pressure oscillations with a delay time. Frequency and decay (or growth) rates are calculated for various combustor design and operating parameters to demonstrate the influence of various parameters on stability. Changes in oxidizer design parameters had a much larger influence on stability than a similar change in fuel parameters. A complete description of the computer program used to make these calculations is given in an appendix.
A real time adaptive controller was designed and tested successfully on a fourth order laboratory dynamic system which features very low structural damping and a noncolocated actuator sensor pair. The controller, implemented in a digital minicomputer, consists of a state estimator, a set of state feedback gains, and a frequency locked loop (FLL) for real time parameter identification. The FLL can detect the closed loop natural frequency of the system being controlled, calculate the mismatch between a plant parameter and its counterpart in the state estimator, and correct the estimator parameter in real time. The adaptation algorithm can correct the controller error and stabilize the system for more than 50% variation in the plant natural frequency, compared with a 10% stability margin in frequency variation for a fixed gain controller having the same performance at the nominal plant condition. After it has locked to the correct plant frequency, the adaptive controller works as well as the fixed gain controller does when there is no parameter mismatch. The very rapid convergence of this adaptive system is demonstrated experimentally, and can also be proven with simple root locus methods.
A fully automated two-way time and frequency transfer (TWSTFT) system including a satellite simulator, which allows the user to carry out signal delay measurements in conjunction with each time transfer measurement, is operated at the Technical University of Graz (TUG). After a brief description of the system, results obtained during fifteen months of operation are presented and discussed. Finally, envisaged experiments are mentioned.